42 
SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
without irrelevant assumptions, can possibly be constructed — the system to the base a *, 
based on the hypothesis that in chemical transformations the unit of hydrogen is an 
“ undistributed ” or “ simple weight,” and the system to the base a 2 , based on the assump- 
tion that the unit of hydrogen is constituted of two simple weights into which that unit 
is distributed in those transformations. These systems are mutually exclusive, and 
cannot both be true. Now we are not in a position to assert that the one of these 
systems is true and the other false. If so, one system would be applicable and the other 
inapplicable to the facts, and in the construction of our system we should get rid of 
hypothesis altogether. It is rarely, however, indeed that in any case such a scientific 
construction is practicable. But failing this, and admitting the inadequacy of our 
information, we may still ask, can we give a reasonable preference to the one or the 
other system 1 Even this might be out of our power. To what extent, too, is this 
preference to be carried % These are questions of probable reasoning which must be 
left to the judgment of individuals ; but if we are to assume these questions to be decided 
before we begin to consider them, we may as well not consider them at all. 
I may first observe that the two systems are not at the outset placed upon a precisely 
equal footing ; for it is certain that in a very large proportion of chemical events the 
Unit of Hydrogen X + 2^— 
„ Chlorine X+2^|^, 
„ Hydrochloric acid . . . X + ^^-f-^?^; 
Y 
whence, putting a as the symbol of the simple weight X, m' as the symbol of the simple weight and \ as 
z 
the symbol of the simple weight we arrive at the equation 
2a' = a'-sr' 2 + od\ 2 . 
This system was pointed out to me, at the time of the appearance of the first part of this memoir, by Professor 
Gr. Stokes ; it was subsequently noticed by Professor Crum Brown (‘ Philosophical Magazine ’ for August 1867), 
and again, more recently, by Professor Clifford in a paper read before the British Association at the Meeting 
in Belfast, 1874. 
This system contains one indeterminate symbol, that is to say, the symbol of one simple weight which cannot 
he determined from the data given in the equation. If we had before us merely the single equation just con- 
sidered, we could not possibly say, without an arbitrary (and therefore unmeaning) assumption, to which of the 
two special systems it was to be referred ; and the only rational course to pursue would be to express the result 
in the indeterminate system, thus keeping both hypotheses before us. But the case is different when we come 
to consider the expression of the total system of chemical equations, which afford us the means of selection with 
probability, although not with certainty, between the two determinate systems. 
* In Part I. Sec. YII. (1) I have termed a the “ modulus ” of the symbolic system, it being that symbol by 
which the form of every other symbol of the system is regulated. As I have occasion to use the term “ modulus ” 
for another purpose, this use of it would give rise to ambiguity, and I shall substitute for it the term “ base.’’ 
